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C2×D5865 #37553365

order23460
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11730
direct productC2×D5865
unambiguous semidirect product(C2×C3)⋊D1955
unambiguous semidirect product(C2×C5)⋊D1173
unambiguous semidirect product(C2×C17)⋊D345
unambiguous semidirect product(C2×C23)⋊D255

Splittings

Fitting, socleC2×C3×C5×C17×C23 ⋊ C2
derived, HallC3×C5×C17×C23 ⋊ C22
HallC5×C17×C23 ⋊ C2×D3
HallC3×C17×C23 ⋊ C2×D5
HallC17×C23 ⋊ C2×D15
HallC3×C5×C23 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D23
HallC5×C23 ⋊ C2×D51
HallC5×C17 ⋊ C2×D69
HallC3×C23 ⋊ C2×D85
HallC3×C17 ⋊ C2×D115
SylowC23 ⋊ C2×D255
SylowC17 ⋊ C2×D345
HallC3×C5 ⋊ C2×D391
SylowC5 ⋊ C2×D1173
SylowC3 ⋊ C2×D1955

Subgroups

subgroupG/H
center, hypercenterC2D5865
commutator, cosocle, hypocenterC3×C5×C17×C23C22
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C23C2
LCSG ▷ C3×C5×C17×C23
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 11730

A minimal faithful permutation representation — 2 generators on 50 points:

(1,2)(3,4,5)(6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50);(4,5)(7,10)(8,9)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(29,50)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)

Conjugacy classes & character table

5868 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23460
maximal normal subgroup ofD23460
maximal quotient ofDic11730, D23460

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 92);